midterm 2006

1
midterm 2006

• Q1 January-mean SLP and UL patterns around the
  North Pacific
• the next 5 slides gives clues towards answering
  Q1

2
SL pressure NH winter
3
1000 mb temperature, NH winter departure from
zonal mean
-15
11
keep the magnitude of the zonal anomalies in mind
4
500 mb height NH winter
note the seasonal-mean trofs, coincident with the
cold anomalies at low levels
5
500 mb height (zonal anomaly) NH winter
two quasi-stationary trofs ? wavenumber 2 pattern
6
Wind _at_300 mb, NH winter
m s-1
m s-1
7
Q1b depth of Siberian cold pool, assuming
hydrostatic balance

• key is that you examine a difference between
  Siberia and normal.
• from previous Figs, we find dT-15K, dp20 mb
  over Siberia (about 1033 mb over Siberia, and
  1013 mb on average). Define Tn and pn the
  normal sea-level temperature and pressure.
• unknown the top of the cold pool (zt). At zt,
  the pressure pt is unperturbed (uniform
  everywhere)
• integrate hydrostatic balance from pt to p at sea
  level, for normal and Siberia conditions. For
  simplicity, assume T(z) constant at low levels.
  Then take the ratio of the two to omit the
  unknown pt.
• normal
  Siberia

8
Q2 Rossby radius of deformation

• a)
• b) LR 200 H/(2p) where LR and H are in km,
  so for H10 km, LR300 km.
• c) Features smaller in scale than LR are
  dominated by buoyancy forcing, resulting in
  gravity waves in a stable environment, so they
  disperse and have a short lifetime. Some energy
  remains in a small vortex. The height field never
  achieves balance, so an initial depression
  vanishes almost entirely.

9
Q3 frontogenesis near tropopause

• right
• vertical
• bottom right reason is the large positive dq/dy
  above the westerly jet
• bottom
• vertical component dw/dy dq/dp reduces dq/dy
  (opposes frontogenesis)
  horizontal component allows the zonal
  wind to restore thermal wind balance (Du/Dt
  fva)
• PV increases north of the westerly jet (stability
  increase) and a PV anomaly couplet forms around
  the developing easterly jet (Pgt0 to the south
  and Plt0 to the north)

10
Zonal-mean wind, 80ºW, troposphere and lower
stratosphere
11
Q4.

• We discussed in class that according to IPV
  thinking, a warm pool forming north of a E-W
  mountain range in the northern hemisphere travels
  eastward. Observations indicate that when an
  alpine lee cyclone form in northern Italy, on the
  south side of the Alps, it also tends to move off
  to the east rapidly. Why? Use IPV thinking.
  Assume a basic state q distribution, . Draw the
  typical low-level q distribution during alpine
  lee cyclogenesis, with cold air pouring south
  west of the Alps, and a pocket of warm air
  remaining in northern Italy.

12
Q5. In the QG framework, why does vertical motion
w occur?

• Answer the vertical motion (and the associated
  ageostrophic, divergent flow) is a response to
  departures from the twin constraints of
  hydrostatic and geostrophic balance. In the QG
  framework, only geostrophic advection is allowed.
  Geostrophic advection of temperature and
  vorticity tend to destroy thermal wind balance.
  The vertical motion then is a direct result of
  departures from geostrophic and/or hydrostatic
  balance, and it aims to restore hydrostatic
  balance, while the associated horizontal flow
  aims to restore geostrophic wind balance.

Q6. What term dominates upward motion forcing,
according to the omega eqn ?

• Answer the dominant term is absolute vorticity
  advection by the thermal wind. It can be
  visualized by plotting absolute vorticity over
  the thickness field. See Holton p 165-166

Q7. What defines the QG framework ?
13
Q8. You want to know vertical motion associated
with a developing winter storm moving to the
northeast at 20 m/s. What fields would you plot
on an isentropic map (eg the 300 K surface) to
graphically infer vertical motion

• calculate V-C (u-us,v-vs) where (us,vs) is the
  storm motion C20(cos(45),sin(45))
• plot this storm-relative motion as wind barbs or
  vectors on the 300K surface, together with p
  (pressure) contours.
• see Dr. J. Moores MetEd module Isentropic
  Analysis, section 6, p5 and p6

Q9. There has been a lot of discussion of the
North Atlantic Oscillation (NAO) lately because
for some time it was remarkably negative. Why is
it that after some time, for instance 2 weeks, a
simple statistical model (consisting of
regression equations) does better in predicting
the behavior of low-frequency variations such as
the NAO, than a full-fledged dynamical model such
as the GFS?

• After some 2 weeks, the spatial distribution of
  diabatic heating, especially in the ITCZ regions,
  is predicted better in a simple statistical model
  (such as the linear inverse model, LIM) than in a
  full dynamical model (see Dr. Sardeshmukhs MetEd
  module should synopticians worry about climate,
  Section 3, p.1 and p2). This spatial distribution
  is affected by large-scale, low-frequency
  variations, and the LIM is built around such
  teleconnecting patterns. Errors in tropical
  heating have world-wide implications. GFS
  continues to produce mid-latitude disturbances
  and the magnitude of meridional energy transfer
  is correct, but the phase and intensity of
  individual baroclinic storms becomes erroneous.